Interfacial thermal stress analysis of an elliptic inclusion with a compliant interphase layer in plane elasticity

Stresses induced by thermal mismatch are known to be a major cause of failure in a wide variety of composite materials and devices ranging from metal–ceramic composites to passivated interconnect lines in integrated circuits. One of the most effective procedures used to reduce these thermal stresses is the addition of a compliant intermediate or interphase layer between the different material components. This paper is concerned with the interfacial thermal stress analysis of an elliptic inclusion embedded within an infinite matrix with uniform change in temperature. A compliant interphase layer is assumed to occupy the region between the inclusion and the matrix. This interphase layer is modeled as a spring layer with vanishing thickness (henceforth referred to as the interface between the inclusion and the matrix). Its behavior is based on the assumption that tractions are continuous but displacements are discontinuous across the interface. Complex variable techniques are used to obtain infinite series representations of the thermal stresses which, when evaluated numerically, demonstrate how the peak interfacial thermal stresses vary with the aspect ratio of the inclusion and the parameter h describing the interface. In addition, and perhaps most significantly, for different aspect ratios of the elliptic inclusion, we identify a specific value (h*) of the interface parameter h which corresponds to the maximum peak thermal stress along the inclusion–matrix interface. Similarly, for different aspect ratios, we identify a specific value of h (also referred to as h* in the paper) which corresponds to the peak maximum thermal strain energy density along the interface (J. Appl. Mech. 57 (1990) 956–963). In each case, we plot the relationship between the new parameter h* and the aspect ratio of the ellipse. This gives significant and valuable information regarding the failure of the interface using two established failure criteria.